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Open Graphs and Computational Reasoning

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Original languageEnglish
Title of host publicationProceedings Sixth Workshop on Developments in Computational Models: Causality, Computation, and Physics, Edinburgh, Scotland, 9-10th July 2010
EditorsS. Barry Cooper, Prakash Panangaden, Elham Kashefi
PublisherOpen Publishing Association
Pages169-180
Number of pages12
DOIs
StatePublished - 2010

Publication series

NameElectronic Proceedings in Theoretical Computer Science
PublisherOpen Publishing Association
Volume26

Abstract

We present a form of algebraic reasoning for computational objects which are expressed as graphs. Edges describe the flow of data between primitive operations which are represented by vertices. These graphs have an interface made of half-edges (edges which are drawn with an unconnected end) and enjoy rich compositional principles by connecting graphs along these half-edges. In particular, this allows equations and rewrite rules to be specified between graphs. Particular computational models can then be encoded as an axiomatic set of such rules. Further rules can be derived graphically and rewriting can be used to simulate the dynamics of a computational system, e.g. evaluating a program on an input. Examples of models which can be formalised in this way include traditional electronic circuits as well as recent categorical accounts of quantum information.

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